Greer is the founder of Camillus Health Concern, which provides health care to thousands of homeless patients in Miami. He also founded St. John Bosco Clinic, which provides services for disadvantaged patients in Little Havana. Greer has previously been awarded a MacArthur Genius Grant.

He is assistant dean of academic affairs at Florida International University's College of Medicine. Greer was formerly assistant dean for homeless education at the University of Miami School of Medicine.